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Uniform Asymptotic Bounds for the Heat Kernel and the Trace of a Stochastic Geodesic Flow
University of Bonn, Institute of Applied Mathematics.
Linnéuniversitetet, Fakultetsnämnden för naturvetenskap och teknik, Institutionen för datavetenskap, fysik och matematik, DFM.
University of Warwick, Department of Statistics.
2012 (engelsk)Inngår i: Stochastics: An International Journal of Probablitiy and Stochastic Processes, ISSN 1744-2508, E-ISSN 1744-2516, Vol. 84, nr 2-3, s. 315-333Artikkel i tidsskrift (Fagfellevurdert) Published
Abstract [en]

We analyze the asymptotic behaviour of the heat kernel dened by a stochastically perturbedgeodesic ow on the cotangent bundle of a Riemannian manifold for small time and smalldiusion parameter. This extends WKB-type methods to a particular case of a degenerateHamiltonian. We give uniform bounds for the solution of the degenerate Hamiltonian boundaryvalue problem for small time. The results are exploited to derive two sided estimates andmultiplicative asymptotics for the heat kernel semigroup and its trace.

sted, utgiver, år, opplag, sider
2012. Vol. 84, nr 2-3, s. 315-333
Emneord [en]
Asymptotic expansions, heat kernel, stochastic geodesic ow, trace formula
HSV kategori
Forskningsprogram
Naturvetenskap, Matematik
Identifikatorer
URN: urn:nbn:se:lnu:diva-7705DOI: 10.1080/17442508.2010.519029ISI: 000303571000013Scopus ID: 2-s2.0-84860329759OAI: oai:DiVA.org:lnu-7705DiVA, id: diva2:345078
Konferanse
International Conference on Stochastic Analysis and Applications Location: Hammamet, TUNISIA Date: OCT 12-17, 2009
Merknad

Online first 09 Jun 2011

Tilgjengelig fra: 2010-08-23 Laget: 2010-08-23 Sist oppdatert: 2017-12-12bibliografisk kontrollert

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Stochastics: An International Journal of Probablitiy and Stochastic Processes

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